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C (Cross) FamilyIn the Cross family, one checker is played on the far side, and one checker is played jumping over the bar. The ratios Far:Down:Jump:Inside = 1:0:1:0.In your position, there are two ways to play on the far side: 24/22 and 23/20. When 24/22 is played on the far side, there are two ways to play a 3 while jumping over the bar: 9/6 and 8/5. When 23/20 is played on the far side, there is only one way to play a 2 while jumping over the bar: 8/6. Thus, there are three members in the Cross family. To rank them, note that no member in the Cross family hits or results in any change in the arrangement of owned points. That means that the 6pt Convention of the Hit/More/Six rule will be the decider. In this case, there is no need to rank all the plays. The moves that place a checker squarely on the 6pt will rank at the top: 24/22 9/6 (your play) and 23/20 8/6. So which gets top billing? To find out, check the destination of the other checker. The play that moves it closer to the 6pt ranks higher.
B (Both) FamilyIn the B (Both) family for non-doublets, one checker is played on the far side, and one checker is played entirely within the outer board. Any move that plays down from the midpoint while moving on the far side belongs in the S (Split) or Z (Reverse split) family.In your position, there is only one way to play in the outer board: 9/7. After moving 9/7, there is only one way to play a 3 on the far side: 23/20. Thus, there is only one play in the B (Both) family.
O (Outer) FamilyIn the O (Outer) family, one checker is played down (to or within the outer board), and one checker is played jumping over the bar. The ratios Far:Down:Jump:Inside = 0:1:1:0.In your position, there are three ways to play down: 13/11, 13/10 and 9/7. When 13/11 is played down, there are two ways to jump over the bar: 9/6 and 8/5. When 13/10 is played down, there is only one way to jump over the bar: 8/6. When 9/7 is played down, there is only one way to jump over the bar: 8/5. Thus, there are four plays in the O (Outer) family. To rank them, note that no member in the Outer family hits or results in any change in the arrangement of owned points. That means that the 6pt Convention of the Hit/More/Six rule will be the decider. In this case, there is no need to rank all the plays. The moves that place a checker squarely on the 6pt will rank at the top: 13/11 9/6 and 13/10 8/6. So which gets top billing? To find out, check the destination of the other checker. The play that leaves it farther back in the outer board ranks higher.
A (Attack) FamilyIn the A (Attack) family, one checker is played inside the home board, and one checker is played jumping over the bar. The ratios Far:Down:Jump:Inside = 0:0:1:1.In your position, there are three ways to jump over the bar: 9/6, 8/6 and 8/5. When 9/6 is played jumping over the bar, there is only one way to play a 2 inside: 6/4. When 8/6 is played jumping over the bar, there is no legal way to play a 3 inside. When 8/5 is played jumping over the bar, there is only one way to play a 2 inside: 6/4. Thus there are two plays in the A (Attack) family. To rank them, note that no member in the Attack family hits or results in any change in the arrangement of owned points. That means that the 6pt Convention of the Hit/More/Six rule will be the decider. The move that places a checker squarely on the 6pt will rank at the top: 9/6 6/4. This is an example where an intermediate checker destination is key to the ranking. Even though no checker is permanently placed on the 6pt, it still counts as a destination for purposes of Hit/More/Six. That is because a checker stops there temporarily on its way to the 4pt.
As always, your Nactation is excellent. The only incorrect one was 23/20 9/6, where you erred by including a member of the S or Z family in the B family. Thanks for posting your rollout. The more the merrier! Mike | ||||||||||||
